{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 机器学习100天——第3天：多元线性回归（Multiple Linear Regression）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第1步：数据预处理"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**导入库**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**导入数据集**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "X:\n[[165349.2 136897.8 471784.1 'New York']\n [162597.7 151377.59 443898.53 'California']\n [153441.51 101145.55 407934.54 'Florida']\n [144372.41 118671.85 383199.62 'New York']\n [142107.34 91391.77 366168.42 'Florida']\n [131876.9 99814.71 362861.36 'New York']\n [134615.46 147198.87 127716.82 'California']\n [130298.13 145530.06 323876.68 'Florida']\n [120542.52 148718.95 311613.29 'New York']\n [123334.88 108679.17 304981.62 'California']]\nY:\n[192261.83 191792.06 191050.39 182901.99 166187.94 156991.12 156122.51\n 155752.6  152211.77 149759.96 146121.95 144259.4  141585.52 134307.35\n 132602.65 129917.04 126992.93 125370.37 124266.9  122776.86 118474.03\n 111313.02 110352.25 108733.99 108552.04 107404.34 105733.54 105008.31\n 103282.38 101004.64  99937.59  97483.56  97427.84  96778.92  96712.8\n  96479.51  90708.19  89949.14  81229.06  81005.76  78239.91  77798.83\n  71498.49  69758.98  65200.33  64926.08  49490.75  42559.73  35673.41\n  14681.4 ]\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "   R&D Spend  Administration  Marketing Spend       State     Profit\n",
       "0  165349.20       136897.80        471784.10    New York  192261.83\n",
       "1  162597.70       151377.59        443898.53  California  191792.06\n",
       "2  153441.51       101145.55        407934.54     Florida  191050.39\n",
       "3  144372.41       118671.85        383199.62    New York  182901.99\n",
       "4  142107.34        91391.77        366168.42     Florida  166187.94"
      ],
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>R&amp;D Spend</th>\n      <th>Administration</th>\n      <th>Marketing Spend</th>\n      <th>State</th>\n      <th>Profit</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>165349.20</td>\n      <td>136897.80</td>\n      <td>471784.10</td>\n      <td>New York</td>\n      <td>192261.83</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>162597.70</td>\n      <td>151377.59</td>\n      <td>443898.53</td>\n      <td>California</td>\n      <td>191792.06</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>153441.51</td>\n      <td>101145.55</td>\n      <td>407934.54</td>\n      <td>Florida</td>\n      <td>191050.39</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>144372.41</td>\n      <td>118671.85</td>\n      <td>383199.62</td>\n      <td>New York</td>\n      <td>182901.99</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>142107.34</td>\n      <td>91391.77</td>\n      <td>366168.42</td>\n      <td>Florida</td>\n      <td>166187.94</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "metadata": {},
     "execution_count": 57
    }
   ],
   "source": [
    "dataset = pd.read_csv('../datasets/50_Startups.csv')\n",
    "X = dataset.iloc[ : , :-1].values\n",
    "Y = dataset.iloc[ : ,  4 ].values\n",
    "Z = dataset.iloc[ : ,  0 ].values\n",
    "print(\"X:\")\n",
    "print(X[:10])\n",
    "print(\"Y:\")\n",
    "print(Y)\n",
    "dataset.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[165349.2 136897.8 471784.1 'New York']\n [162597.7 151377.59 443898.53 'California']\n [153441.51 101145.55 407934.54 'Florida']\n [144372.41 118671.85 383199.62 'New York']\n [142107.34 91391.77 366168.42 'Florida']\n [131876.9 99814.71 362861.36 'New York']\n [134615.46 147198.87 127716.82 'California']\n [130298.13 145530.06 323876.68 'Florida']\n [120542.52 148718.95 311613.29 'New York']\n [123334.88 108679.17 304981.62 'California']\n [101913.08 110594.11 229160.95 'Florida']\n [100671.96 91790.61 249744.55 'California']\n [93863.75 127320.38 249839.44 'Florida']\n [91992.39 135495.07 252664.93 'California']\n [119943.24 156547.42 256512.92 'Florida']\n [114523.61 122616.84 261776.23 'New York']\n [78013.11 121597.55 264346.06 'California']\n [94657.16 145077.58 282574.31 'New York']\n [91749.16 114175.79 294919.57 'Florida']\n [86419.7 153514.11 224494.78489361703 'New York']\n [76253.86 113867.3 298664.47 'California']\n [78389.47 153773.43 299737.29 'New York']\n [73994.56 122782.75 303319.26 'Florida']\n [67532.53 105751.03 304768.73 'Florida']\n [77044.01 99281.34 140574.81 'New York']\n [64664.71 139553.16 137962.62 'California']\n [75328.87 144135.98 134050.07 'Florida']\n [72107.6 127864.55 353183.81 'New York']\n [66051.52 182645.56 118148.2 'Florida']\n [65605.48 153032.06 107138.38 'New York']\n [61994.48 115641.28 91131.24 'Florida']\n [61136.38 152701.92 88218.23 'New York']\n [63408.86 129219.61 46085.25 'California']\n [55493.95 103057.49 214634.81 'Florida']\n [46426.07 157693.92 210797.67 'California']\n [46014.02 85047.44 205517.64 'New York']\n [28663.76 127056.21 201126.82 'Florida']\n [44069.95 51283.14 197029.42 'California']\n [20229.59 65947.93 185265.1 'New York']\n [38558.51 82982.09 174999.3 'California']\n [28754.33 118546.05 172795.67 'California']\n [27892.92 84710.77 164470.71 'Florida']\n [23640.93 96189.63 148001.11 'California']\n [15505.73 127382.3 35534.17 'New York']\n [22177.74 154806.14 28334.72 'California']\n [1000.23 124153.04 1903.93 'New York']\n [1315.46 115816.21 297114.46 'Florida']\n [76793.34958333334 135426.92 224494.78489361703 'California']\n [542.05 51743.15 224494.78489361703 'New York']\n [76793.34958333334 116983.8 45173.06 'California']]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.impute import SimpleImputer\n",
    "imputer = SimpleImputer(missing_values=0.0, strategy=\"mean\")\n",
    "imputer = imputer.fit(X[ : , 0:3])\n",
    "X[ : , 0:3] = imputer.transform(X[ : , 0:3])\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**将类别数据数字化**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "original:\n[[165349.2 136897.8 471784.1 'New York']\n [162597.7 151377.59 443898.53 'California']\n [153441.51 101145.55 407934.54 'Florida']\n [144372.41 118671.85 383199.62 'New York']\n [142107.34 91391.77 366168.42 'Florida']\n [131876.9 99814.71 362861.36 'New York']\n [134615.46 147198.87 127716.82 'California']\n [130298.13 145530.06 323876.68 'Florida']\n [120542.52 148718.95 311613.29 'New York']\n [123334.88 108679.17 304981.62 'California']]\nlabelencoder:\n[[165349.2 136897.8 471784.1 2]\n [162597.7 151377.59 443898.53 0]\n [153441.51 101145.55 407934.54 1]\n [144372.41 118671.85 383199.62 2]\n [142107.34 91391.77 366168.42 1]\n [131876.9 99814.71 362861.36 2]\n [134615.46 147198.87 127716.82 0]\n [130298.13 145530.06 323876.68 1]\n [120542.52 148718.95 311613.29 2]\n [123334.88 108679.17 304981.62 0]]\nonehot:\n[[0.0 0.0 1.0 165349.2 136897.8 471784.1]\n [1.0 0.0 0.0 162597.7 151377.59 443898.53]\n [0.0 1.0 0.0 153441.51 101145.55 407934.54]\n [0.0 0.0 1.0 144372.41 118671.85 383199.62]\n [0.0 1.0 0.0 142107.34 91391.77 366168.42]\n [0.0 0.0 1.0 131876.9 99814.71 362861.36]\n [1.0 0.0 0.0 134615.46 147198.87 127716.82]\n [0.0 1.0 0.0 130298.13 145530.06 323876.68]\n [0.0 0.0 1.0 120542.52 148718.95 311613.29]\n [1.0 0.0 0.0 123334.88 108679.17 304981.62]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import LabelEncoder, OneHotEncoder\n",
    "from sklearn.compose import ColumnTransformer \n",
    "labelencoder = LabelEncoder()\n",
    "print(\"original:\")\n",
    "print(X[:10])\n",
    "#print(X[: , 3])\n",
    "X[: , 3] = labelencoder.fit_transform(X[ : , 3])\n",
    "#print(X[: , 3])\n",
    "print(\"labelencoder:\")\n",
    "print(X[:10])\n",
    "ct = ColumnTransformer([( \"encoder\", OneHotEncoder(), [3])], remainder = 'passthrough')\n",
    "X = ct.fit_transform(X)\n",
    "#onehotencoder = OneHotEncoder(categorical_features = [3])\n",
    "#X = onehotencoder.fit_transform(X).toarray()\n",
    "print(\"onehot:\")\n",
    "print(X[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**躲避虚拟变量陷阱**\n",
    "\n",
    "在回归预测中我们需要所有的数据都是numeric的，但是会有一些非numeric的数据，比如国家，省，部门，性别。这时候我们需要设置虚拟变量（Dummy variable）。做法是将此变量中的每一个值，衍生成为新的变量，是设为1，否设为0.举个例子，“性别”这个变量,我们可以虚拟出“男”和”女”两虚拟变量，男性的话“男”值为1，”女”值为0；女性的话“男”值为0，”女”值为1。\n",
    "\n",
    "但是要注意，这时候虚拟变量陷阱就出现了。就拿性别来说，其实一个虚拟变量就够了，比如 1 的时候是“男”， 0 的时候是”非男”，即为女。如果设置两个虚拟变量“男”和“女”，语义上来说没有问题，可以理解，但是在回归预测中会多出一个变量，多出的这个变量将会对回归预测结果产生影响。一般来说，如果虚拟变量要比实际变量的种类少一个。 \n",
    "\n",
    "在多重线性回归中，变量不是越多越好，而是选择适合的变量。这样才会对结果准确预测。如果category类的特征都放进去，拟合的时候，所有权重的计算，都可以有两种方法实现，一种是提高某个category的w，一种是降低其他category的w，这两种效果是等效的，也就是发生了共线性,虚拟变量系数相加和为1，出现完全共线陷阱。\n",
    "\n",
    "**但是下面测试尽然和想法不一致。。。**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "X1 = X[: , 1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[0.0 1.0 165349.2 136897.8 471784.1]\n [0.0 0.0 162597.7 151377.59 443898.53]\n [1.0 0.0 153441.51 101145.55 407934.54]\n [0.0 1.0 144372.41 118671.85 383199.62]\n [1.0 0.0 142107.34 91391.77 366168.42]\n [0.0 1.0 131876.9 99814.71 362861.36]\n [0.0 0.0 134615.46 147198.87 127716.82]\n [1.0 0.0 130298.13 145530.06 323876.68]\n [0.0 1.0 120542.52 148718.95 311613.29]\n [0.0 0.0 123334.88 108679.17 304981.62]\n [1.0 0.0 101913.08 110594.11 229160.95]\n [0.0 0.0 100671.96 91790.61 249744.55]\n [1.0 0.0 93863.75 127320.38 249839.44]\n [0.0 0.0 91992.39 135495.07 252664.93]\n [1.0 0.0 119943.24 156547.42 256512.92]\n [0.0 1.0 114523.61 122616.84 261776.23]\n [0.0 0.0 78013.11 121597.55 264346.06]\n [0.0 1.0 94657.16 145077.58 282574.31]\n [1.0 0.0 91749.16 114175.79 294919.57]\n [0.0 1.0 86419.7 153514.11 224494.78489361703]\n [0.0 0.0 76253.86 113867.3 298664.47]\n [0.0 1.0 78389.47 153773.43 299737.29]\n [1.0 0.0 73994.56 122782.75 303319.26]\n [1.0 0.0 67532.53 105751.03 304768.73]\n [0.0 1.0 77044.01 99281.34 140574.81]\n [0.0 0.0 64664.71 139553.16 137962.62]\n [1.0 0.0 75328.87 144135.98 134050.07]\n [0.0 1.0 72107.6 127864.55 353183.81]\n [1.0 0.0 66051.52 182645.56 118148.2]\n [0.0 1.0 65605.48 153032.06 107138.38]\n [1.0 0.0 61994.48 115641.28 91131.24]\n [0.0 1.0 61136.38 152701.92 88218.23]\n [0.0 0.0 63408.86 129219.61 46085.25]\n [1.0 0.0 55493.95 103057.49 214634.81]\n [0.0 0.0 46426.07 157693.92 210797.67]\n [0.0 1.0 46014.02 85047.44 205517.64]\n [1.0 0.0 28663.76 127056.21 201126.82]\n [0.0 0.0 44069.95 51283.14 197029.42]\n [0.0 1.0 20229.59 65947.93 185265.1]\n [0.0 0.0 38558.51 82982.09 174999.3]\n [0.0 0.0 28754.33 118546.05 172795.67]\n [1.0 0.0 27892.92 84710.77 164470.71]\n [0.0 0.0 23640.93 96189.63 148001.11]\n [0.0 1.0 15505.73 127382.3 35534.17]\n [0.0 0.0 22177.74 154806.14 28334.72]\n [0.0 1.0 1000.23 124153.04 1903.93]\n [1.0 0.0 1315.46 115816.21 297114.46]\n [0.0 0.0 76793.34958333334 135426.92 224494.78489361703]\n [0.0 1.0 542.05 51743.15 224494.78489361703]\n [0.0 0.0 76793.34958333334 116983.8 45173.06]]\n[[0.0 0.0 1.0 165349.2 136897.8 471784.1]\n [1.0 0.0 0.0 162597.7 151377.59 443898.53]\n [0.0 1.0 0.0 153441.51 101145.55 407934.54]\n [0.0 0.0 1.0 144372.41 118671.85 383199.62]\n [0.0 1.0 0.0 142107.34 91391.77 366168.42]\n [0.0 0.0 1.0 131876.9 99814.71 362861.36]\n [1.0 0.0 0.0 134615.46 147198.87 127716.82]\n [0.0 1.0 0.0 130298.13 145530.06 323876.68]\n [0.0 0.0 1.0 120542.52 148718.95 311613.29]\n [1.0 0.0 0.0 123334.88 108679.17 304981.62]\n [0.0 1.0 0.0 101913.08 110594.11 229160.95]\n [1.0 0.0 0.0 100671.96 91790.61 249744.55]\n [0.0 1.0 0.0 93863.75 127320.38 249839.44]\n [1.0 0.0 0.0 91992.39 135495.07 252664.93]\n [0.0 1.0 0.0 119943.24 156547.42 256512.92]\n [0.0 0.0 1.0 114523.61 122616.84 261776.23]\n [1.0 0.0 0.0 78013.11 121597.55 264346.06]\n [0.0 0.0 1.0 94657.16 145077.58 282574.31]\n [0.0 1.0 0.0 91749.16 114175.79 294919.57]\n [0.0 0.0 1.0 86419.7 153514.11 224494.78489361703]\n [1.0 0.0 0.0 76253.86 113867.3 298664.47]\n [0.0 0.0 1.0 78389.47 153773.43 299737.29]\n [0.0 1.0 0.0 73994.56 122782.75 303319.26]\n [0.0 1.0 0.0 67532.53 105751.03 304768.73]\n [0.0 0.0 1.0 77044.01 99281.34 140574.81]\n [1.0 0.0 0.0 64664.71 139553.16 137962.62]\n [0.0 1.0 0.0 75328.87 144135.98 134050.07]\n [0.0 0.0 1.0 72107.6 127864.55 353183.81]\n [0.0 1.0 0.0 66051.52 182645.56 118148.2]\n [0.0 0.0 1.0 65605.48 153032.06 107138.38]\n [0.0 1.0 0.0 61994.48 115641.28 91131.24]\n [0.0 0.0 1.0 61136.38 152701.92 88218.23]\n [1.0 0.0 0.0 63408.86 129219.61 46085.25]\n [0.0 1.0 0.0 55493.95 103057.49 214634.81]\n [1.0 0.0 0.0 46426.07 157693.92 210797.67]\n [0.0 0.0 1.0 46014.02 85047.44 205517.64]\n [0.0 1.0 0.0 28663.76 127056.21 201126.82]\n [1.0 0.0 0.0 44069.95 51283.14 197029.42]\n [0.0 0.0 1.0 20229.59 65947.93 185265.1]\n [1.0 0.0 0.0 38558.51 82982.09 174999.3]\n [1.0 0.0 0.0 28754.33 118546.05 172795.67]\n [0.0 1.0 0.0 27892.92 84710.77 164470.71]\n [1.0 0.0 0.0 23640.93 96189.63 148001.11]\n [0.0 0.0 1.0 15505.73 127382.3 35534.17]\n [1.0 0.0 0.0 22177.74 154806.14 28334.72]\n [0.0 0.0 1.0 1000.23 124153.04 1903.93]\n [0.0 1.0 0.0 1315.46 115816.21 297114.46]\n [1.0 0.0 0.0 76793.34958333334 135426.92 224494.78489361703]\n [0.0 0.0 1.0 542.05 51743.15 224494.78489361703]\n [1.0 0.0 0.0 76793.34958333334 116983.8 45173.06]]\n"
     ]
    }
   ],
   "source": [
    "print(X1)\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**拆分数据集为训练集和测试集**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[[0.0 1.0 0.0 66051.52 182645.56 118148.2]\n [1.0 0.0 0.0 100671.96 91790.61 249744.55]\n [0.0 1.0 0.0 101913.08 110594.11 229160.95]\n [0.0 1.0 0.0 27892.92 84710.77 164470.71]\n [0.0 1.0 0.0 153441.51 101145.55 407934.54]\n [0.0 0.0 1.0 72107.6 127864.55 353183.81]\n [0.0 0.0 1.0 20229.59 65947.93 185265.1]\n [0.0 0.0 1.0 61136.38 152701.92 88218.23]\n [0.0 1.0 0.0 73994.56 122782.75 303319.26]\n [0.0 1.0 0.0 142107.34 91391.77 366168.42]]\n[103282.38 144259.4  146121.95  77798.83 191050.39 105008.31  81229.06\n  97483.56 110352.25 166187.94]\n[[1.0 0.0 66051.52 182645.56 118148.2]\n [0.0 0.0 100671.96 91790.61 249744.55]\n [1.0 0.0 101913.08 110594.11 229160.95]\n [1.0 0.0 27892.92 84710.77 164470.71]\n [1.0 0.0 153441.51 101145.55 407934.54]\n [0.0 1.0 72107.6 127864.55 353183.81]\n [0.0 1.0 20229.59 65947.93 185265.1]\n [0.0 1.0 61136.38 152701.92 88218.23]\n [1.0 0.0 73994.56 122782.75 303319.26]\n [1.0 0.0 142107.34 91391.77 366168.42]]\n[103282.38 144259.4  146121.95  77798.83 191050.39 105008.31  81229.06\n  97483.56 110352.25 166187.94]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size = 0.2, random_state = 0)\n",
    "X1_train, X1_test, Y1_train, Y1_test = train_test_split(X1, Y, test_size = 0.2, random_state = 0)\n",
    "print(X_test)\n",
    "print(Y_test)\n",
    "print(X1_test)\n",
    "print(Y1_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第2步：在训练集上训练多元线性回归模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "metadata": {},
     "execution_count": 64
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "regressor = LinearRegression()\n",
    "regressor.fit(X_train, Y_train)\n",
    "regressor1 = LinearRegression()\n",
    "regressor1.fit(X1_train, Y1_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第3步：在测试集上预测结果¶"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = regressor.predict(X_test)\n",
    "y1_pred = regressor1.predict(X1_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "[102388.94113041 121465.72713517 127340.57708619  71709.47538912\n 174211.0848     121771.65061494  68393.54360668  95588.5313349\n 116596.3467699  162514.07218551]\n[102388.94113046 121465.72713518 127340.57708619  71709.47538916\n 174211.08479987 121771.65061482  68393.5436067   95588.53133498\n 116596.34676982 162514.07218541]\n"
     ]
    }
   ],
   "source": [
    "print(y_pred)\n",
    "print(y1_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**完整的项目请前往Github项目100-Days-Of-ML-Code查看。有任何的建议或者意见欢迎在issue中提出~**"
   ]
  }
 ],
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